Shashwat Singh

Prof. Brian L. Stuart

CS 164-A

November 21, 2016

Babbage Difference Engine Simulation

A difference engine is an automatic mechanical calculator designed to tab- ulate polynomial functions. The name derives from the method of divided differ- ences, a way to interpolate or tabulate functions by using a small set of polyno- mial coefficients. Most mathematical functions commonly used by engineers, sci- entists and navigators, including logarithmic and trigonometric functions, can be approximated by polynomials, so a difference engine can compute many useful tables of numbers. The historical difficulty in producing error-free tables by teams of mathematicians and human "computers" spurred Charles Babbage's desire to build a mechanism to automate the process. It is considered to be the world's first computer. Difference Engine Simulator ( Javascript ):

Approach:

• I created around 8-9 variables to store different values and assigned them to the various input boxes.

• Then I created a new ‘calculate()’ function and assigned it to the start button. Inside the calculate() function are inputs gathered from text boxes are assigned inside parseInt() and ParseFloat().

• Then I used ‘for’ loop inside the ‘calculate’ function in order to process and calculate the values, thus storing and outputting the values shown in the text box.

How it works:

• Initially there are total of 8 text boxes in the simulator.

• User must fill numbers in them and press the start button to com- pute.

• When the start button is pressed, the calculation will output in the large text box under the input fields with the number of rows mentioned in the “rows” input box.

• To re-start the whole process, user can press the reload button. Test:

• Attached below is the screenshot for the values given in the as- signment up to 100 rows.

• In addition to this, it was also tested with y = x4 ( — here derivatives are : y=0, ∆y = 0, ∆2y = 0 , ∆3y = 0, ∆4y = 24, ∆5y = 0 ) Data for y = x4

00000240

100024240

2002448240

30247272240

4249614496240

5120240240120240

6360480360144240

7840840504168240 816801344672192240

930242016864216240

10 5040 2880 1080 240 24 0

11 7920 3960 1320 264 24 0

12 11880 5280 1584 288 24 0

13 17160 6864 1872 312 24 0

14 24024 8736 2184 336 24 0

15 32760 10920 2520 360 24 0

16 43680 13440 2880 384 24 0

17 57120 16320 3264 408 24 0

18 73440 19584 3672 432 24 0

19 93024 23256 4104 456 24 0

20 116280 27360 4560 480 24 0

Simulator Link — http://www.pages.drexel.edu/~ss4335/engine.html References :

Difference Engine Intro. In Wikipedia. Retrieved November 20th 2016, from https://en.wikipedi- a.org/wiki/Difference_engine